• Recent Problems

    Write 2014 with the first four prime numbers, with the aid of the operations addition, multiplication and exponentiation.
    Grades: 6th to 8th, 3rd to 5th
    Algebraic Thinking
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Gain familiarity with factors and multiples.
    Multiply and divide within 100.
    3.OA.C.7, 4.OA.B.4, 6.EE.A.1
    On the map shown, begin at Start. Travel the roads along any path you like, following typical traffic laws, and each time you pass a number, add it to your current sum. However, you are not allowed to pass any number more than once. Can you reach End with a sum of 91?
    Grades: 3rd to 5th
    Num & Ops Base Ten
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    3.NBT.A.2, 4.NBT.B.4



    A magic rectangle is an m× n array of the positive integers from 1 to m× n such that the numbers in each row have a constant sum and the numbers in each column have a constant sum (although the row sum need not equal the column sum). Shown below is a 3 × 5 magic rectangle with the integers 1-15.


     Two of three arrays at left can be filled with the integers 1-24 to form a magic rectangle. Which one can't, and why not? 


    Let A =  1, B =  2, and so on, with each letter equal to its position in the alphabet. The lexivalue of a word is the sum of the values of its letters. For example, ROMANS has a lexivalue of 18 + 15 + 13 + 1 + 14 + 19 =  80.

    Now, do the following:

    • Pick a number.
    • Convert it into its representation in Roman numerals.
    • Find the lexivalue for that Roman numeral.

    For example, if you choose 11, that becomes XI in Roman numerals, and XI has a lexivalue of 24 + 9 =  33.

    Are there any numbers for which the lexivalue is equal to the original number?

    A figure resembling a spiral is shown with 35 matches. Move 4 matches to form 3 squares.
    Grades: 6th to 8th
    Draw construct, and describe geometrical figures and describe the relationships between them.
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